The main type of rational approximants that we will employ as fitting functions
are the standard Padé approximants (PAs). We recall that a PA
\(P_N^M(z)\)  is a ratio of two polynomials of orders \(M\)  and
\(N\)  [1]}, [2]}, i.e.,
\(P_N^M(z) = \dfrac{Q_M(z)}{R_N(z)} =\dfrac{a_0 + a_1 \, z + a_2 \, z^2 + \dots + a_M \, z^M}{1 + b_1 \, z + b_2 \, z^2 + \dots + b_N \, z^N} \; ,\) 
